Some signs that your three-year-old may be developmentally delayed include if they're not walking, if they're not talking.
At this age 75% of their speech should be understood. Well if you are not understanding half of what they're saying, that's cause for concern. If your child is not engaged which means if they're not looking at you, if they're not responding to you, if you're not able to have them follow simple instructions, if they're not pointing to objects that they know, that is cause for concern.
If ever your child loses a skill that they once had, things like they were able to talk to you and say simple phrases and now no longer do that, that is cause for concern. And lastly, anytime you feel that something may be off and you have that gut reaction and there's an instinct that something may be off with my child don't delay.
Speak with your child's pediatrician and share with him or her your concerns with your child's development and they will tell you whether or not there's cause for concern.